X-Git-Url: https://git.donarmstrong.com/?a=blobdiff_plain;f=kinetic_formalism.Rnw;h=683f29f005d219f5b2ef1aefe360993ea98b0d42;hb=8bcb93ccb71a8a2f830c42cf1ae7408c42b5dc24;hp=1ed5a8bbe0515edefe0649230f16af69f0928ce4;hpb=34ab2dce170021ce3d2452dff699a9c95dbc35e5;p=ool%2Flipid_simulation_formalism.git

diff --git a/kinetic_formalism.Rnw b/kinetic_formalism.Rnw
index 1ed5a8b..683f29f 100644
--- a/kinetic_formalism.Rnw
+++ b/kinetic_formalism.Rnw
@@ -62,6 +62,11 @@
 <<results=hide,echo=FALSE>>=
 require(lattice)
 require(grid)
+# R in cal / mol K
+to.kcal <- function(k,temp=300) {
+  gasconst <- 1.985
+  return(gasconst*temp*log(k)/1000)
+}
 @ 
 
 \section{State Equation}
@@ -112,6 +117,14 @@ curve(2^x,from=0,to=sd(c(0,4)),
       ylab="Unsaturation Forward Adjustment")
 @ 
 
+<<fig=TRUE,echo=FALSE,results=hide,width=5,height=5>>=
+curve(to.kcal(2^x),from=0,to=sd(c(0,4)),
+      main="Unsaturation forward",
+      xlab="Standard Deviation of Unsaturation of Vesicle",
+      ylab="Unsaturation Forward (k cal)")
+@ 
+
+
 \newpage
 \subsubsection{Charge Forward}
 \begin{equation}
@@ -133,6 +146,21 @@ print(wireframe(z~x*y,grid,cuts=50,
 rm(x,y,grid)
 @ 
 
+<<fig=TRUE,echo=FALSE,results=hide,width=7,height=7>>=
+x <- seq(-1,0,length.out=20)
+y <- seq(-1,0,length.out=20)
+grid <- expand.grid(x=x,y=y)
+grid$z <- as.vector(to.kcal(60^(-outer(x,y))))
+print(wireframe(z~x*y,grid,cuts=50,
+          drape=TRUE,
+          scales=list(arrows=FALSE),
+          xlab=list("Average Vesicle Charge",rot=30),
+          ylab=list("Component Charge",rot=-35),
+          zlab=list("Charge Forward (k cal)",rot=93)))
+rm(x,y,grid)
+@ 
+
+
 \newpage
 \subsubsection{Curvature Forward}
 \begin{equation}
@@ -149,6 +177,16 @@ curve(10^x,from=0,to=max(c(sd(abs(log(c(0.8,1.33)))),
       ylab="Curvature Forward Adjustment")
 @ 
 
+<<fig=TRUE,echo=FALSE,results=hide,width=7,height=5>>=
+curve(to.kcal(10^x),from=0,to=max(c(sd(abs(log(c(0.8,1.33)))),
+                    sd(abs(log(c(1,1.33)))),
+                    sd(abs(log(c(0.8,1)))))),
+      main="Curvature forward",
+      xlab="Standard Deviation of Absolute value of the Log of the Curvature of Vesicle",
+      ylab="Curvature Forward Adjustment (kcal)")
+@ 
+
+
 \newpage
 \subsubsection{Length Forward}
 \begin{equation}
@@ -163,6 +201,14 @@ curve(3^x,from=0,to=sd(c(12,24)),
       ylab="Length Forward Adjustment")
 @ 
 
+<<fig=TRUE,echo=FALSE,results=hide,width=7,height=5>>=
+curve(to.kcal(3^x),from=0,to=sd(c(12,24)),
+      main="Length forward",
+      xlab="Standard Deviation of Length of Vesicle",
+      ylab="Length Forward Adjustment (kcal)")
+@ 
+
+
 \subsubsection{Complex Formation}
 \begin{equation}
   CF1_f=1
@@ -196,6 +242,20 @@ print(wireframe(z~x*y,grid,cuts=50,
 rm(grid)
 @ 
 
+<<fig=TRUE,echo=FALSE,results=hide,width=7,height=7>>=
+grid <- expand.grid(x=seq(0,4,length.out=20),
+                    y=seq(0,4,length.out=20))
+grid$z <- to.kcal(10^(abs(3.5^-grid$x-3.5^-grid$y)))
+print(wireframe(z~x*y,grid,cuts=50,
+          drape=TRUE,
+          scales=list(arrows=FALSE),
+          xlab=list("Average Vesicle Unsaturation",rot=30),
+          ylab=list("Monomer Unsaturation",rot=-35),
+          zlab=list("Unsaturation Backward (kcal)",rot=93)))
+rm(grid)
+@ 
+
+
 \newpage
 \subsubsection{Charge Backwards}
 \begin{equation}
@@ -217,10 +277,24 @@ print(wireframe(z~x*y,grid,cuts=50,
 rm(x,y,grid)
 @ 
 
+<<fig=TRUE,echo=FALSE,results=hide,width=7,height=7>>=
+x <- seq(-1,0,length.out=20)
+y <- seq(-1,0,length.out=20)
+grid <- expand.grid(x=x,y=y)
+grid$z <- to.kcal(as.vector(20^(outer(x,y))))
+print(wireframe(z~x*y,grid,cuts=50,
+          drape=TRUE,
+          scales=list(arrows=FALSE),
+          xlab=list("Average Vesicle Charge",rot=30),
+          ylab=list("Component Charge",rot=-35),
+          zlab=list("Charge Backwards (kcal)",rot=93)))
+rm(x,y,grid)
+@ 
+
 \newpage
 \subsubsection{Curvature Backwards}
 \begin{equation}
-  cu_f = 7^{1-\left(20\left(\log cu_\mathrm{vesicle}-\log cu_\mathrm{monomer}\right)^2+1\right)^{-1}}
+  cu_f = 7^{1-\left(20\left(\log_{e} cu_\mathrm{vesicle}-\log_{e} cu_\mathrm{monomer}\right)^2+1\right)^{-1}}
   \label{eq:curvature_backwards}
 \end{equation}
 
@@ -237,6 +311,20 @@ print(wireframe(z~x*y,grid,cuts=50,
 rm(grid)
 @ 
 
+<<fig=TRUE,echo=FALSE,results=hide,width=7,height=7>>=
+grid <- expand.grid(x=seq(0.8,1.33,length.out=20),
+                    y=seq(0.8,1.33,length.out=20))
+grid$z <- to.kcal(7^(1-1/(20*(log(grid$x)-log(grid$y))^2+1)))
+print(wireframe(z~x*y,grid,cuts=50,
+          drape=TRUE,
+          scales=list(arrows=FALSE),
+          xlab=list("Vesicle Curvature",rot=30),
+          ylab=list("Monomer Curvature",rot=-35),
+          zlab=list("Curvature Backward (kcal)",rot=93)))
+rm(grid)
+@ 
+
+
 \newpage
 \subsubsection{Length Backwards}
 \begin{equation}
@@ -257,6 +345,20 @@ print(wireframe(z~x*y,grid,cuts=50,
 rm(grid)
 @ 
 
+<<fig=TRUE,echo=FALSE,results=hide,width=7,height=7>>=
+grid <- expand.grid(x=seq(12,24,length.out=20),
+                    y=seq(12,24,length.out=20))
+grid$z <- to.kcal(3.2^(abs(grid$x-grid$y)))
+print(wireframe(z~x*y,grid,cuts=50,
+          drape=TRUE,
+          scales=list(arrows=FALSE),
+          xlab=list("Average Vesicle Length",rot=30),
+          ylab=list("Monomer Length",rot=-35),
+          zlab=list("Length Backward (kcal)",rot=93)))
+rm(grid)
+@ 
+
+
 \newpage
 \subsubsection{Complex Formation Backward}
 \begin{equation}
@@ -277,6 +379,20 @@ print(wireframe(z~x*y,grid,cuts=50,
 rm(grid)
 @ 
 
+<<fig=TRUE,echo=FALSE,results=hide,width=7,height=7>>=
+grid <- expand.grid(x=seq(-1,3,length.out=20),
+                    y=seq(-1,3,length.out=20))
+grid$z <- to.kcal(3.2^(grid$x*grid$y-abs(grid$x*grid$y)))
+print(wireframe(z~x*y,grid,cuts=50,
+          drape=TRUE,
+          scales=list(arrows=FALSE),
+          xlab=list("Vesicle Complex Formation",rot=30),
+          ylab=list("Monomer Complex Formation",rot=-35),
+          zlab=list("Complex Formation Backward (kcal)",rot=93)))
+rm(grid)
+@ 
+
+